First of all, there are differences between edge and blade geometry.
For Blades:
Flat grinds are ground against a flat surface called a platen. Hollow grinds are ground against a contact wheel so a concave scoop is actually taken out of the blade. A convex grind is done on a slack belt grinder. Both sides of the blade slope convexly towards the edge. A saber grind is a flat or hollow grind that goes half way up the blade, leaving the top half of the blade full thickness and flat. All things being equal, a convex grind is strongest but has the leash sharp edge, a hollow grind can have the sharpest edge (and is easy to sharpen) but it is the weakest. A flat grind is a compromise in the middle.
Chisel grinding is where one side of the blade is ground while the other isn't. For fighting blades this can be good as it leaves wound channels that have a harder time closing in on themselves. If you are a righty and want to do utility work with a chisel grind, it is best to have the unground side facing you, or lese the knife will have a tendency to curve into the cut.
Edge grinds are flat, hollow or convex. They have the same advantages/disadvantages as listed above. But combining blade and edge geometry is where magic happens. Chris Reeve does a high hollow grind on the Sebenza folder and convex grinds the edge. THere is a thin edge there (thanks to the hollow blade grind) and it is strengthened by convex grinding the edge.
Typically people also talk about point geometry, but I'll leave that for now, unless you ask for that info.
Good luck and welcome to the forums.